The England international has recently found himself axed from the Sky Blues’ first-team after enduring an error-strewn start to the season.
Pellegrini has been searching for an alternative for some time, and appears to have now settled on Neuer.
The German stopper is widely regarded as one of the top goalkeepers on the planet, and was a key member of Bayern’s Champions League and Bundesliga double last term.
Neuer is said to be valued at around £40m, and rumours suggest City are ready to stump up such a fee and make him the highest paid number one in the game with a weekly salary of £105,000.
A January move appears unlikely, with the Premier League giants ready to wait until the end of the season to weigh up whether or not the ‘keeper will be assessing his options.
Pellegrini is thought to be willing to splash out for a new option in the short-term, with La Liga duo Willy Caballero and Claudio Bravo at the top of his wish list.